AES E-Library

Time-Alignment of Multi-Way Speakers with Group Delay Equalization - I

In this paper, a first of two-parts, a technique for time-aligning
the driver responses (viz., woofer, mid-range, and tweeter
responses) in a multi-way speaker system is presented. Generally,
woofers exhibit a much larger time-of-arrival delay, at a
listening position, compared to the mid-range and high-frequency
drivers. Moreover, the time-of-arrival delay for all drivers is
frequency dependent exhibiting a large variation over the audible
frequency domain. Due to these differences, a two-part study was
undertaken to understand the effects of these variations,
quantitatively and qualitatively. In this first part, we present
the motivation behind the system used for applying all-pass
filters to process audio signals being delivered to the multi-way
speaker and propose a time-delay difference equalization
technique. We show that applying all-pass filters result in
significant ``temporal-smearing' of the response, despite
flattening of the group delay response. Thus depending on the
amount of group-delay equalization, the smearing with pre-ring
effects could potentially have audible effects depending on the
content. However, despite the temporal-smearing (viz.,
response-dilation in time) for an arbitrary-order all-pass filter,
we show that the time-frequency characteristics of these
group-delay equalizing filters exhibit a uniform decay rate at
all-frequencies allowing group-delay equalization without
affecting the modal decay rates. Thus this enables other cascaded
filter structures to be utilized for modal equalization in
additional to conventional loudspeaker-room equalizers. We also
propose group-delay flattening for the woofer and a small range of
the midrange frequencies through a weighted approach at the lower
frequencies for group-delay equalization. Future work will involve
investigations using perceptually motivated variable-octave
complex smoothing of responses (1/24-th octave smoothing at low
frequencies and 1/3-rd octave at higher frequencies), and
designing all-pass filters based on this phase-smoothed data.
Quantitative results obtained will be presented in this paper,
whereas the next part of the two-part paper will present results
from listening tests.